Question
$$x(x+1)(x+2)(x+3)\frac{x+4}{120} = 100$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x(x+1)(x+2)(x+3)\frac{x+4}{120} &= 100&& \text{multiply ALL terms by } \color{blue}{ 120 }. \\[1 em]120x(x+1)(x+2)(x+3)\frac{x+4}{120} &= 120\cdot100&& \text{cancel out the denominators} \\[1 em]x^5+10x^4+35x^3+50x^2+24x &= 12000&& \text{move all terms to the left hand side } \\[1 em]x^5+10x^4+35x^3+50x^2+24x-12000 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
This page was created using
Polynomial Equations Solver